61 research outputs found
Noise-based information processing: Noise-based logic and computing: what do we have so far?
We briefly introduce noise-based logic. After describing the main motivations
we outline classical, instantaneous (squeezed and non-squeezed), continuum,
spike and random-telegraph-signal based schemes with applications such as
circuits that emulate the brain functioning and string verification via a slow
communication channel.Comment: Invited talk at the 21st International Conference on Noise and
Fluctuations, Toronto, Canada, June 12-16, 201
Quantum Algorithmic Gate-Based Computing: Grover Quantum Search Algorithm Design in Quantum Software Engineering
The difference between classical and quantum algorithms (QA) is following:
problem solved by QA is coded in the structure of the quantum operators. Input
to QA in this case is always the same. Output of QA says which problem coded.
In some sense, give a function to QA to analyze and QA returns its property as
an answer without quantitative computing. QA studies qualitative properties of
the functions. The core of any QA is a set of unitary quantum operators or
quantum gates. In practical representation, quantum gate is a unitary matrix
with particular structure. The size of this matrix grows exponentially with an
increase in the number of inputs, which significantly limits the QA simulation
on a classical computer with von Neumann architecture. Quantum search algorithm
(QSA) - models apply for the solution of computer science problems as searching
in unstructured data base, quantum cryptography, engineering tasks, control
system design, robotics, smart controllers, etc. Grovers algorithm is explained
in details along with implementations on a local computer simulator. The
presented article describes a practical approach to modeling one of the most
famous QA on classical computers, the Grover algorithm.Comment: arXiv admin note: text overlap with arXiv:quant-ph/0112105 by other
author
Kvantu automātu un meklēšanas algoritmu iespējas un ierobežojumi
Kvantu skaitļošana ir nozare, kas pēta uz kvantu mehānikas likumiem balstīto
skaitļošanas modeļu īpašības. Disertācija ir veltīta kvantu skaitļošanas
algoritmiskiem aspektiem. Piedāvāti rezultāti trijos virzienos:
Kvantu galīgi automāti
Analizēta stāvokļu efektivitāte kvantu vienvirziena galīgam automātam.
Uzlabota labāka zināmā eksponenciālā atšķirība [AF98] starp
kvantu un klasiskajiem galīgajiem automātiem.
Grovera algoritma analīze
Pētīta Grovera algoritma noturība pret kļūdām. Vispārināts [RS08]
loģisko kļūdu modelis un piedāvāti vairāki jauni rezultāti.
Kvantu klejošana
Pētīta meklēšana 2D režģī izmantojot kvantu klejošanu. Paātrināts
[AKR05] kvantu klejošanas meklēšanas algoritms.
Atslēgas vārdi: Kvantu galīgi automāti, eksponenciālā atšķirība, Grovera
algoritms, noturība pret kļūdām, kvantu klejošana
LITERATŪRA
[AF98] A. Ambainis, R. Freivalds.
1-way quantum finite automata: strengths, weaknesses and generalizations.
Proceedings of the 39th IEEE Conference on Foundations of
Computer Science, 332-341, 1998.
arXiv:quant-ph/9802062v3
[AKR05] A. Ambainis, J. Kempe, A. Rivosh.
Coins make quantum walks faster.
Proceedings of SODA’05, 1099-1108, 2005.
[RS08] O. Regev, L. Schiff. Impossibility of a Quantum Speed-up with
a Faulty Oracle.
Proceedings of ICALP’2008, Lecture Notes in Computer Science,
5125:773-781, 2008.Quantum computation is the eld that investigates properties of models of
computation based on the laws of the quantum mechanics. The thesis is ded-
icated to algorithmic aspects of quantum computation and provides results
in three directions:
Quantum nite automata
We study space-eciency of one-way quantum nite automata. We
improve best known exponential separation [AF98] between quantum
and classical one-way nite automata.
Analysis of Grover's algorithm
We study fault-tolerance of Grover's algorithm. We generalize the
model of logical faults by [RS08] and present several new results.
Quantum walks
We study search by quantum walks on two-dimensional grid. We im-
prove (speed-up) quantum walk search algorithm by [AKR05].
Keywords: Quantum nite automata, exponential separation, Grover's al-
gorithm, fault-tolerance, quantum walks
BIBLIOGRAPHY
[AF98] A. Ambainis, R. Freivalds.
1-way quantum nite automata: strengths, weaknesses and gen-
eralizations.
Proceedings of the 39th IEEE Conference on Foundations of
Computer Science, 332-341, 1998.
arXiv:quant-ph/9802062v3
[AKR05] A. Ambainis, J. Kempe, A. Rivosh.
Coins make quantum walks faster.
Proceedings of SODA'05, 1099-1108, 2005.
[RS08] O. Regev, L. Schi. Impossibility of a Quantum Speed-up with
a Faulty Oracle.
Proceedings of ICALP'2008, Lecture Notes in Computer
Science, 5125:773-781, 2008
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Quantum Algorithm for Continuous Global Optimization
We investigate the entwined roles of information and quantum algorithms in reducing the complexity of the global optimization problem (GOP). We show that: (1) a modest amount of additional information is sufficient to map the general continuous GOP into the (discrete) Grover problem; (2) while this additional information is actually available in some classes of GOPs, it cannot be taken advantage of within classical optimization algorithms; (3) on the contrary, quantum algorithms over a natural framework for the efficient use of this information resulting in a speed-up of the solution of the GOP
Instantaneous noise-based logic
We show two universal, Boolean, deterministic logic schemes based on binary
noise timefunctions that can be realized without time-averaging units. The
first scheme is based on a new bipolar random telegraph wave scheme and the
second one makes use of the recent noise-based logic which is conjectured to be
the brain's method of logic operations [Physics Letters A 373 (2009)
2338-2342]. Error propagation and error removal issues are also addressed.Comment: Accepted for publication in Fluctuation and Noise Letters (December
2010 issue
Shallow Depth Factoring Based on Quantum Feasibility Labeling and Variational Quantum Search
Large integer factorization is a prominent research challenge, particularly
in the context of quantum computing. This holds significant importance,
especially in information security that relies on public key cryptosystems. The
classical computation of prime factors for an integer has exponential time
complexity. Quantum computing offers the potential for significantly faster
computational processes compared to classical processors. In this paper, we
propose a new quantum algorithm, Shallow Depth Factoring (SDF), to factor a
biprime integer. SDF consists of three steps. First, it converts a factoring
problem to an optimization problem without an objective function. Then, it uses
a Quantum Feasibility Labeling (QFL) method to label every possible solution
according to whether it is feasible or infeasible for the optimization problem.
Finally, it employs the Variational Quantum Search (VQS) to find all feasible
solutions. The SDF utilizes shallow-depth quantum circuits for efficient
factorization, with the circuit depth scaling linearly as the integer to be
factorized increases. Through minimizing the number of gates in the circuit,
the algorithm enhances feasibility and reduces vulnerability to errors.Comment: 10 pages, 3 figure
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